G.P Thomson Experiment

After the experiments on diffraction of electrons by C. J. Davisson and L. H. Germer, G. P. Thomson, the son of J. J. Thomson, also replicated the experiment on electron diffraction in 1927.

Electrons from an electron source were accelerated towards a positive electrode into which a small hole was drilled. The resulting narrow beam of electrons was directed towards a thin, rolled foil of gold. After passing through the hole in the gold foil, the electron beam was received on a photographic plate placed perpendicular to the direction of the beam. The diffraction pattern was in the form of continuous, alternate black and white rings as diffraction was due to the crystalline grains which were randomly oriented at all possible angles in the gold foil. The diffraction rings had narrowly defined radii and always seemed to occur in multiples i.e. circles of radii 2r,\,3r\, … They were similar to the sharply defined principle maxima of the intensity pattern for -slits. Here the planes of atoms in the crystal act as slits. The radii of the different sets of rings were found to correspond precisely to the spacing of the various planes of atoms. Electrons were scattered at different angles from the atoms of crystallites and produced interference pattern with maxima corresponding to those angles satisfying the Bragg condition. In terms of the probabilistic interpretation of matter waves, the probability of finding an electron scattered at an angle \theta\, is exactly equal to computed intensity pattern of interfering waves associated with electron beam.

The diffraction pattern due to poly crystalline material was similar to the powder diffraction pattern of X-rays having wavelength equal to the de Broglie wavelength of electrons. The wavelength of electrons was varied by changing the incident energy of the electrons, then diameters of the diffraction rings changed proportionately according to the Bragg’s equation.

Experimental set-up b) Diffraction pattern using X-rays c) Diffraction pattern using electrons

When crystalline sample of aluminium was used, the diffraction pattern changed to spots lying around a ring-like structure.

For Aluminium, the spacing between atomic planes d=2.34\, Å..

According to the N-slit interference formula, the n^{th}\, -order principle maximum occurs at angle \theta\,. Bragg’s condition is

     G.P Thomson Experiment

k \,d\, sin\, \theta=2\pi\, n. (Wavenumber G.P Thomson Experiment

     G.P Thomson Experiment

for n=1\, (i.e. the first-order principle maximum).

From the experimental observations it is found that k\, depends on the voltage V\, as

     k \alpha \sqrt V.

For electron having mass m\,, velocity v\,, momentum p\,, Kinetic Energy KE\, the relations are

     KE=\frac{1}{2}mv^2=\frac{1}{2}m\left(\frac{p}{m}\right)^2=\frac{p^2}{2m}.
     KE\,=\,eV
     p=\sqrt{2meV}.
     p \alpha \sqrt V

Momentum p\, is controlled by the voltage V\,.

Thus p\, and k\, both are proportional to  V^{1/2}\,

     k=\frac{p}{\hbar},  

( \hbar is the constant of proportionality)

This is the relation between two intrinsic properties and Momentum p\, of electrons.

     \hbar=p/k

By substituting the values for the constants m,\,e and using the relation

     m=9.11\times 10^{-31} kg,               e=1.602\times 10^{-19}C

Value of the proportionality constant \hbar\, comes out to be about {1 \times 10^{-34}} J s,

This value is quite close to the official value of \hbar\, which is a universal constant of nature known as reduced Planck’s constant and given by

\hbar=1.005...\times 10^{-34} J.s

Thus the de Broglie’s relation and his hypothesis of matter waves are verified.

G.P. Thomson and C. J. Davisson shared the Nobel Prize in 1937 for their independent experiments which proved that electrons (material particles) show wave-like behavior. It is interesting to note that G.P. Thompson was the son of J.J. Thomson who received the Nobel Prize in 1906 for proving that cathode rays were actually particles – electrons!

Significance of Experiments on Diffraction

After the discovery of Bragg’s law in 1915, it was being applied to study the atomic structure using diffraction of X-rays which are waves. To apply it to study the diffraction of electrons which are particles was an extremely novel idea. Davisson and Germer as well as G.P. Thomson used it for the first time in their separate experiments. Their experiments proved independently the wave-like behavior of electron (i.e. matter) and confirmed quantitatively the de Broglie hypothesis of matter waves. These experiments proved that de Broglie’s waves are not just mathematical tools, but exhibit real physical effects which can be observed in the laboratory. Just as Compton had showed that X-rays (i.e. waves) could show particle-like behavior, these classic experiments on electron diffraction showed that electrons (i.e. particles) show wave-like behavior. It established the wave-particle duality or the dual nature of matter.

Davisson and Thomson were jointly awarded Nobel Prize in Physics in 1937 for their fundamental work.

 

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